Maps that do not have a linear mapping to real world space (latitude, longitude, and altitude, or other measurements in the physical world) are very common and useful, but can be difficult to use with generic software systems. Examples of such non-linear maps include: subway maps, ski-maps, industrial diagrams and infrastructure diagrams (e.g. maps of power grids, telecommunications grids and wide area transportation maps).
On such irregularly spaced non-linear maps, spaces get compressed, stretched, rotated, and otherwise distorted. The nature of these distortions also often varies within the map itself, with different regions of the map being distorted in different ways. For instance, one region may be stretched, another may be compressed, and still another region may be rotated—or a combination thereof—and so on.
Because these non-linear maps present an irregular representation of physical space, they are able to convey a great deal of useful information in a small display. However it is difficult to display real world location data on top of non-linear maps because the mapping from latitude, longitude, and altitude (or other physical world coordinate systems) to a position on such irregularly spaced maps is complex and irregular. At least two key difficulties arise: (1) the ability to map real-world locations onto the irregularly spaced maps, (2) the ability to map points on the irregularly spaced maps into physical world coordinates.
Certain techniques can be used for extrapolating the location of map-points on top of non-linear, irregularly spaced maps. Typically these techniques work by attempting to extrapolate location data from nearby points, but this can be complex, time consuming, and error-prone—particularly in systems where the map's data is irregularly spaced. Thus, it would be advantageous to provide other techniques that allow users to make the design-time and run-timeuse of non-linear mapping techniques that are fast, simple, and accessible to moderately skilled programmers and other individuals who are not experts in map-design, complex math or cartography.